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tresset_1 [31]
2 years ago
7

Solve |x - 6| + 8 = 17

Mathematics
2 answers:
Nesterboy [21]2 years ago
7 0

Answer:

x=15

Step-by-step explanation:

(x-6)+8=17 then remove unnecessary parentheses x-6+8=17 then calculate the sum x + 2 = 17 the move constant to the right hand side and change its sign x = 17 - 2 then subtract the numbers x=15 btw you should use photo math that's what I used

Anettt [7]2 years ago
4 0

|x - 6| + 8 = 17

Subtract 8 from both sides.

|x - 6| + 8 - 8 = 17 - 8

|x - 6| = 9

Set x - 6 to 9 and -9, which leads to two cases.

x - 6 = 9

x = 9 + 6

x = 15

x - 6 = -9

x = -9 + 3

x = -6

Which is the answer?

Plug both values into the original absolute value equation to see which yields a true statement.

Let x = 15

|15 - 6| + 8 = 17

|9| + 8 = 17

9 + 8 = 17

17 = 17

Let x = -6

|-6 - 6| + 8 = 17

|-12| + 8 = 17

12 + 8 = 17

20 DOES NOT EQUAL 17.

Answer: x = 15

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Let a, b, c, and d be real numbers with a, c 6= 0. Prove that the lines y = ax+b and y = cx + d have the same x-intercept if and
Monica [59]

Step-by-step explanation:

We have got the lines :

y=ax+b\\y=cx+d

Both lines intercept the x-axis in the point :

I = (i_{1} ,i_{2})

In all point from x-axis the y-component is equal to 0.

I=(i_{1},o)

We replace the I point in the lines equations:

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0=a(i_{1})+b \\-b=a(i_{1})\\i_{1}=\frac{-b}{a}

From the second equation :

0=c(i_{1})+d\\ -d=c(i_{1})\\i_{1}=\frac{-d}{c}

Then i_{1}=i_{1}

Finally :

\frac{-b}{a}=\frac{-d}{c} \\\frac{b}{a}=\frac{d}{c} \\ad=bc

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8 0
3 years ago
Factor completely: 2x4 − 32.
vazorg [7]

Answer:

Option b) is correct.

The completed factor of given expression is  2(x-2)(x+2)(x^2+4)

Step-by-step explanation:

Given expression is 2x^4-32

To find the completed factor for the given expression:

2x^4-32:

Taking the common number "2" outside  to the above expression we get

2x^4-32=2(x^4-16)

Now rewritting the above  expression as below

=2(x^4-2^4)  (since 16 can be written as the number 2 to the power of 4)

=2((x^2)^2-(2^2)^2)

The above expression is of the form a^2-b^2=(a+b)(a-b)

Here a=x^2 and  b=2^2

Therefore it becomes

=2(x^2+2^2)(x^2-2^2)

=2(x^2+4)(x^2-2^2)  

The above expression is of the form a^2-b^2=(a+b)(a-b)

Here a=x and  b=2

Therefore it becomes

=2(x^2+4)(x+2)(x-2)  

=2(x+2)(x-2)(x^2+4)  

Therefore =2(x+2)(x-2)(x^2+4)  

2x^4-32=2(x-2)(x+2)(x^2+4)  

Option b) is correct.

The completed factor of given expression is  2(x-2)(x+2)(x^2+4)

3 0
3 years ago
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